Sinn Fein said an inquiry was now needed after Environment Minister Arlene Foster turned down its request to publish the Planning Service's advice in relation to granting approval for a private developer to take on the project.
The SDLP, meanwhile, called for First Minister Ian Paisley to make a full and frank statement to the Assembly on the matter.
This was after it emerged that DUP leader Ian Paisley wrote an impassioned letter to the Heritage Lottery Fund (HLF) supporting Mr Sweeney's project bid – stating in the correspondence, in 2003, that the international world heritage body UNESCO supported this scheme, a claim disputed by a senior UNESCO official.
The Causeway contract has been mired in allegations of cronyism ever since DUP minister Mrs Foster said she was minded to end the long-running saga of a replacement visitors' centre by agreeing to Mr Sweeney's development.
Mrs Foster has made it clear she did not know Mr Sweeney was a DUP member, has never met him, and has warned she will sue anyone who suggests she acted improperly.
However, there have been suggestions that her indication that Mr Sweeney would get approval for the development may run contrary to recommendations in a Planning Service report.
Sinn Fein wanted all documents and files made public.
Mrs Foster said she could not do this because she did "not believe it would be appropriate to release a copy of the Planning Service report and recommendation".
MLA Daithi McKay said: "Planning Service applications and files are supposed to be open for the public to view and scrutinise. It is imperative that this remains the case if the service is to avoid any claims of corruption or foul play.
"The minister is clearly bringing the entire service into disrepute by refusing to publish these documents and she has failed to give any good reason for that.
"This is a matter of major public interest."
Mr McKay called for an inquiry.
Meanwhile, the DUP's woes on the issue did not subside when it was revealed yesterday that Mr Paisley made representations on Mr Sweeney's behalf to the HLF.
The MP said, in 2003, that Mr Sweeney had the blessing of international world heritage body UNESCO for his Causeway centre scheme.
But the Belfast Telegraph discovered this is disputed by a UNESCO official
In the Paisley letter, on headed House of Commons paper, the MP said: "UNESCO saw and approved the plans, and were very impressed by the proposal."
It is understood that Mr Paisley did meet a UNESCO official to discuss the Causeway situation.
SDLP East Londonderry MLA John Dallat last night said the continuing controversy around Mr Paisley and Ian Paisley Jnr's connections with Mr Sweeney were in danger of bringing the whole Executive into disrepute.
Mr Paisley Jnr bought an apartment from Mr Sweeney, though the transaction was done by the book. And the two men are friends.
But when asked on the Stephen Nolan Show on Radio Ulster if he knew him, Mr Paisley Jnr replied: "I know of him" – fuelling speculation, even though there appears to be no evidence that any DUP members have done anything wrong.